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SSM-Tp’s, l=0

SSM-Thom polynomials up to cohomological degree 16

of

contact singularities of relative dimension l=0 up to codimension 8.

the singularities

codimension 0

Local algebra C
Thom-Boardman class \Sigma^0
Codimension 0
SSM-Thom polynomial in Chern classes 1 -Tc_{1} +T^2c_{1}^2 -T^3c_{1}^3 +T^4(c_{1}^4 +c_{1}c_{3} -c_{2}^2) +T^5( -c_{1}^5 -3c_{1}^2c_{3} +3c_{1}c_{2}^2) +T^6(c_{1}^6 +6c_{1}^3c_{3} -6c_{1}^2c_{2}^2 +c_{1}^2c_{4} -3c_{1}c_{2}c_{3} +2c_{2}^3 +c_{1}c_{5} -4c_{2}c_{4} +3c_{3}^2) +T^7( -c_{1}^7 -10c_{1}^4c_{3} +10c_{1}^3c_{2}^2 -4c_{1}^3c_{4} +12c_{1}^2c_{2}c_{3} -8c_{1}c_{2}^3 -4c_{1}^2c_{5} +16c_{1}c_{2}c_{4} -12c_{1}c_{3}^2) +T^8(c_{1}^8 +15c_{1}^5c_{3} -15c_{1}^4c_{2}^2 +10c_{1}^4c_{4} -30c_{1}^3c_{2}c_{3} +20c_{1}^2c_{2}^3 +11c_{1}^3c_{5} -44c_{1}^2c_{2}c_{4} +30c_{1}^2c_{3}^2 +6c_{1}c_{2}^2c_{3} -3c_{2}^4 +2c_{1}^2c_{6} -10c_{1}c_{2}c_{5} +4c_{1}c_{3}c_{4} +16c_{2}^2c_{4} -12c_{2}c_{3}^2 +c_{1}c_{7} -6c_{2}c_{6} +15c_{3}c_{5} -10c_{4}^2)
SSM-Thom polynomial in Schur functions s_{0} -Ts_{1} +T^2(s_{2} +s_{1,1}) +T^3( -s_{3} -2s_{2,1} -s_{1,1,1}) +T^4(s_{4} +s_{2,2} +3s_{3,1} +3s_{2,1,1} +s_{1,1,1,1}) +T^5( -s_{5} -2s_{3,2} -4s_{4,1} -2s_{2,2,1} -6s_{3,1,1} -4s_{2,1,1,1} -s_{1,1,1,1,1}) +T^6(s_{6} +s_{3,3} +3s_{4,2} +5s_{5,1} +s_{2,2,2} +5s_{3,2,1} +10s_{4,1,1} +3s_{2,2,1,1} +10s_{3,1,1,1} +5s_{2,1,1,1,1} +s_{1,1,1,1,1,1}) +T^7( -s_{7} -2s_{4,3} -4s_{5,2} -6s_{6,1} -3s_{3,2,2} -3s_{3,3,1} -9s_{4,2,1} -15s_{5,1,1} -2s_{2,2,2,1} -9s_{3,2,1,1} -20s_{4,1,1,1} -4s_{2,2,1,1,1} -15s_{3,1,1,1,1} -6s_{2,1,1,1,1,1} -s_{1,1,1,1,1,1,1}) +T^8(s_{1,1,1,1,1,1,1,1} +7s_{2,1,1,1,1,1,1} +5s_{2,2,1,1,1,1} +3s_{2,2,2,1,1} +s_{2,2,2,2} +21s_{3,1,1,1,1,1} +14s_{3,2,1,1,1} +7s_{3,2,2,1} +6s_{3,3,1,1} +3s_{3,3,2} +35s_{4,1,1,1,1} +19s_{4,2,1,1} +6s_{4,2,2} +7s_{4,3,1} +s_{4,4} +35s_{5,1,1,1} +14s_{5,2,1} +3s_{5,3} +21s_{6,1,1} +5s_{6,2} +7s_{7,1} +s_{8})

SSM-Thom polynomial in Schur-tilde functions S_{}

codimension 1

Local algebra C[x]/(x^2)
Thom-Boardman class \Sigma^{1,0}
Codimension 1
SSM-Thom polynomial in Chern classes Tc_{1} +T^2( -2c_{1}^2 -c_{2}) +T^3(3c_{1}^3 +3c_{1}c_{2} +c_{3}) +T^4( -4c_{1}^4 -6c_{1}^2c_{2} -7c_{1}c_{3} +3c_{2}^2 -c_{4}) +T^5(5c_{1}^5 +10c_{1}^3c_{2} +23c_{1}^2c_{3} -13c_{1}c_{2}^2 +9c_{1}c_{4} -4c_{2}c_{3} +c_{5}) +T^6( -6c_{1}^6 -15c_{1}^4c_{2} -54c_{1}^3c_{3} +34c_{1}^2c_{2}^2 -38c_{1}^2c_{4} +25c_{1}c_{2}c_{3} -2c_{2}^3 -17c_{1}c_{5} +24c_{2}c_{4} -13c_{3}^2 -c_{6}) +T^7(7c_{1}^7 +21c_{1}^5c_{2} +105c_{1}^4c_{3} -70c_{1}^3c_{2}^2 +111c_{1}^3c_{4} -90c_{1}^2c_{2}c_{3} +14c_{1}c_{2}^3 +89c_{1}^2c_{5} -144c_{1}c_{2}c_{4} +74c_{1}c_{3}^2 +2c_{2}^2c_{3} +27c_{1}c_{6} -38c_{2}c_{5} +18c_{3}c_{4} +c_{7}) +T^8( -8c_{1}^8 -28c_{1}^6c_{2} -181c_{1}^5c_{3} +125c_{1}^4c_{2}^2 -260c_{1}^4c_{4} +240c_{1}^3c_{2}c_{3} -50c_{1}^2c_{2}^3 -301c_{1}^3c_{5} +509c_{1}^2c_{2}c_{4} -244c_{1}^2c_{3}^2 -14c_{1}c_{2}^2c_{3} -6c_{2}^4 -178c_{1}^2c_{6} +305c_{1}c_{2}c_{5} -135c_{1}c_{3}c_{4} -54c_{2}^2c_{4} +34c_{2}c_{3}^2 -51c_{1}c_{7} +106c_{2}c_{6} -122c_{3}c_{5} +59c_{4}^2 -c_{8})

SSM-Thom polynomial in Schur functions Ts_{1} +T^2( -3s_{2} -2s_{1,1}) +T^3(7s_{3} +9s_{2,1} +3s_{1,1,1}) +T^4( -15s_{4} -11s_{2,2} -28s_{3,1} -18s_{2,1,1} -4s_{1,1,1,1}) +T^5(31s_{5} +48s_{3,2} +75s_{4,1} +32s_{2,2,1} +70s_{3,1,1} +30s_{2,1,1,1} +5s_{1,1,1,1,1}) +T^6( -63s_{6} -51s_{3,3} -153s_{4,2} -186s_{5,1} -28s_{2,2,2} -167s_{3,2,1} -225s_{4,1,1} -65s_{2,2,1,1} -140s_{3,1,1,1} -45s_{2,1,1,1,1} -6s_{1,1,1,1,1,1}) +T^7(127s_{7} +210s_{4,3} +426s_{5,2} +441s_{6,1} +171s_{3,2,2} +211s_{3,3,1} +615s_{4,2,1} +651s_{5,1,1} +77s_{2,2,2,1} +393s_{3,2,1,1} +525s_{4,1,1,1} +112s_{2,2,1,1,1} +245s_{3,1,1,1,1} +63s_{2,1,1,1,1,1} +7s_{1,1,1,1,1,1,1}) +T^8( -8s_{1,1,1,1,1,1,1,1} -84s_{2,1,1,1,1,1,1} -175s_{2,2,1,1,1,1} -151s_{2,2,2,1,1} -58s_{2,2,2,2} -392s_{3,1,1,1,1,1} -768s_{3,2,1,1,1} -532s_{3,2,2,1} -562s_{3,3,1,1} -290s_{3,3,2} -1050s_{4,1,1,1,1} -1641s_{4,2,1,1} -701s_{4,2,2} -981s_{4,3,1} -199s_{4,4} -1736s_{5,1,1,1} -1936s_{5,2,1} -641s_{5,3} -1764s_{6,1,1} -1099s_{6,2} -1016s_{7,1} -255s_{8})

SSM-Thom polynomial in Schur-tilde functions ( -12S_{7,1} -S_{8} -32S_{5,1,1,1} -40S_{6,1,1})T^8 +(8S_{4,1,1,1} +24S_{5,1,1} +10S_{6,1} +S_{7})T^7 +( -12S_{4,1,1} -8S_{5,1} -S_{6})T^6 +(4S_{3,1,1} +6S_{4,1} +S_{5})T^5 +( -4S_{3,1} -S_{4})T^4 +(2S_{2,1} +S_{3})T^3 -T^2S_{2} +TS_{1}

codimension 2

Local algebra C[x]/(x^3)
Thom-Boardman class \Sigma^{1,1,0}
Codimension 2
SSM-Thom polynomial in Chern classes T^2(c_{1}^2 +c_{2}) +T^3( -3c_{1}^3 -6c_{1}c_{2} -3c_{3}) +T^4(6c_{1}^4 +18c_{1}^2c_{2} +20c_{1}c_{3} -c_{2}^2 +7c_{4}) +T^5( -10c_{1}^5 -40c_{1}^3c_{2} -76c_{1}^2c_{3} +11c_{1}c_{2}^2 -56c_{1}c_{4} +6c_{2}c_{3} -15c_{5}) +T^6(15c_{1}^6 +75c_{1}^4c_{2} +211c_{1}^3c_{3} -46c_{1}^2c_{2}^2 +245c_{1}^2c_{4} -39c_{1}c_{2}c_{3} -11c_{2}^3 +152c_{1}c_{5} -53c_{2}c_{4} +22c_{3}^2 +31c_{6}) +T^7( -21c_{1}^7 -126c_{1}^5c_{2} -480c_{1}^4c_{3} +130c_{1}^3c_{2}^2 -776c_{1}^3c_{4} +162c_{1}^2c_{2}c_{3} +54c_{1}c_{2}^3 -795c_{1}^2c_{5} +423c_{1}c_{2}c_{4} -199c_{1}c_{3}^2 +39c_{2}^2c_{3} -400c_{1}c_{6} +199c_{2}c_{5} -79c_{3}c_{4} -63c_{7}) +T^8(28c_{1}^8 +196c_{1}^6c_{2} +953c_{1}^5c_{3} -295c_{1}^4c_{2}^2 +1997c_{1}^4c_{4} -512c_{1}^3c_{2}c_{3} -155c_{1}^2c_{2}^3 +2907c_{1}^3c_{5} -1855c_{1}^2c_{2}c_{4} +907c_{1}^2c_{3}^2 -290c_{1}c_{2}^2c_{3} +39c_{2}^4 +2468c_{1}^2c_{6} -1755c_{1}c_{2}c_{5} +769c_{1}c_{3}c_{4} -93c_{2}^2c_{4} -17c_{2}c_{3}^2 +1052c_{1}c_{7} -742c_{2}c_{6} +440c_{3}c_{5} -119c_{4}^2 +127c_{8})
SSM-Thom polynomial in Schur functions T^2(2s_{2} +s_{1,1}) +T^3( -12s_{3} -12s_{2,1} -3s_{1,1,1}) +T^4(50s_{4} +29s_{2,2} +73s_{3,1} +36s_{2,1,1} +6s_{1,1,1,1}) +T^5( -180s_{5} -218s_{3,2} -340s_{4,1} -119s_{2,2,1} -245s_{3,1,1} -80s_{2,1,1,1} -10s_{1,1,1,1,1}) +T^6(602s_{6} +391s_{3,3} +1137s_{4,2} +1381s_{5,1} +168s_{2,2,2} +1017s_{3,2,1} +1290s_{4,1,1} +314s_{2,2,1,1} +615s_{3,1,1,1} +150s_{2,1,1,1,1} +15s_{1,1,1,1,1,1}) +T^7( -1932s_{7} -2618s_{4,3} -5044s_{5,2} -5180s_{6,1} -1648s_{3,2,2} -2161s_{3,3,1} -5943s_{4,2,1} -5887s_{5,1,1} -610s_{2,2,2,1} -3015s_{3,2,1,1} -3640s_{4,1,1,1} -668s_{2,2,1,1,1} -1295s_{3,1,1,1,1} -252s_{2,1,1,1,1,1} -21s_{1,1,1,1,1,1,1}) +T^8(28s_{1,1,1,1,1,1,1,1} +392s_{2,1,1,1,1,1,1} +1245s_{2,2,1,1,1,1} +1508s_{2,2,2,1,1} +666s_{2,2,2,2} +2422s_{3,1,1,1,1,1} +7126s_{3,2,1,1,1} +6643s_{3,2,2,1} +7226s_{3,3,1,1} +4773s_{3,3,2} +8540s_{4,1,1,1,1} +19553s_{4,2,1,1} +10603s_{4,2,2} +16061s_{4,3,1} +4075s_{4,4} +18508s_{5,1,1,1} +29174s_{5,2,1} +12833s_{5,3} +24584s_{6,1,1} +20401s_{6,2} +18481s_{7,1} +6050s_{8})
SSM-Thom polynomial in Schur-tilde functions (24S_{3,2,1,1,1} +12S_{3,2,2,1} +115S_{3,3,1,1} +18S_{3,3,2} +65S_{4,1,1,1,1} +641S_{4,2,1,1} +116S_{4,2,2} +489S_{4,3,1} +33S_{4,4} +968S_{5,1,1,1} +1928S_{5,2,1} +328S_{5,3} +2060S_{6,1,1} +1228S_{6,2} +1318S_{7,1} +254S_{8})T^8 +( -84S_{3,2,1,1} -20S_{3,2,2} -76S_{3,3,1} -176S_{4,1,1,1} -500S_{4,2,1} -100S_{4,3} -656S_{5,1,1} -428S_{5,2} -554S_{6,1} -126S_{7})T^7 +(5S_{2,2,1,1} +2S_{2,2,2} +19S_{3,1,1,1} +102S_{3,2,1} +19S_{3,3} +180S_{4,1,1} +132S_{4,2} +222S_{5,1} +62S_{6})T^6 +( -12S_{2,2,1} -38S_{3,1,1} -34S_{3,2} -82S_{4,1} -30S_{5})T^5 +(5S_{2,1,1} +5S_{2,2} +26S_{3,1} +14S_{4})T^4 +( -6S_{2,1} -6S_{3})T^3 +(S_{1,1} +2S_{2})T^2

codimension 3

Local algebra C[x]/(x^4)
Thom-Boardman class \Sigma^{1,1,1,0}
Codimension 3
SSM-Thom polynomial in Chern classes (2 c_{3}+ 3 c_{1} c_{2}+ c_{1}^3) T^3+ (-4 T^3(c_{1}^3 +3c_{1}c_{2} +2c_{3}) +T^4( -4c_{1}^4 -18c_{1}^2c_{2} -22c_{1}c_{3} -4c_{2}^2 -12c_{4}) +T^5(10c_{1}^5 +60c_{1}^3c_{2} +116c_{1}^2c_{3} +19c_{1}c_{2}^2 +121c_{1}c_{4} +14c_{2}c_{3} +50c_{5}) +T^6( -20c_{1}^6 -150c_{1}^4c_{2} -414c_{1}^3c_{3} -46c_{1}^2c_{2}^2 -647c_{1}^2c_{4} -94c_{1}c_{2}c_{3} +21c_{2}^3 -544c_{1}c_{5} +3c_{2}c_{4} -29c_{3}^2 -180c_{6}) +T^7(35c_{1}^7 +315c_{1}^5c_{2} +1155c_{1}^4c_{3} +70c_{1}^3c_{2}^2 +2438c_{1}^3c_{4} +355c_{1}^2c_{2}c_{3} -168c_{1}c_{2}^3 +3187c_{1}^2c_{5} -181c_{1}c_{2}c_{4} +382c_{1}c_{3}^2 -147c_{2}^2c_{3} +2219c_{1}c_{6} -251c_{2}c_{5} +195c_{3}c_{4} +602c_{7}) +T^8( -56c_{1}^8 -588c_{1}^6c_{2} -2722c_{1}^5c_{3} -50c_{1}^4c_{2}^2 -7302c_{1}^4c_{4} -968c_{1}^3c_{2}c_{3} +710c_{1}^2c_{2}^3 -13183c_{1}^3c_{5} +1454c_{1}^2c_{2}c_{4} -2315c_{1}^2c_{3}^2 +1293c_{1}c_{2}^2c_{3} -17c_{2}^4 -14496c_{1}^2c_{6} +2987c_{1}c_{2}c_{5} -2523c_{1}c_{3}c_{4} +781c_{2}^2c_{4} +21c_{2}c_{3}^2 -8554c_{1}c_{7} +1858c_{2}c_{6} -1012c_{3}c_{5} -6c_{4}^2 -1932c_{8})
SSM-Thom polynomial in Schur functions (s_{1, 1, 1}+ 5 s_{2, 1}+ 6 s_{3}) T^3+ (-4 T^3(6s_{3} +5s_{2,1} +s_{1,1,1}) +T^4( -60s_{4} -30s_{2,2} -74s_{3,1} -30s_{2,1,1} -4s_{1,1,1,1}) +T^5(390s_{5} +398s_{3,2} +625s_{4,1} +189s_{2,2,1} +375s_{3,1,1} +100s_{2,1,1,1} +10s_{1,1,1,1,1}) +T^6( -2100s_{6} -1158s_{3,3} -3304s_{4,2} -4090s_{5,1} -425s_{2,2,2} -2584s_{3,2,1} -3200s_{4,1,1} -676s_{2,2,1,1} -1260s_{3,1,1,1} -250s_{2,1,1,1,1} -20s_{1,1,1,1,1,1}) +T^7(10206s_{7} +11680s_{4,3} +22046s_{5,2} +23205s_{6,1} +6249s_{3,2,2} +8526s_{3,3,1} +22730s_{4,2,1} +22141s_{5,1,1} +2037s_{2,2,2,1} +9854s_{3,2,1,1} +11375s_{4,1,1,1} +1820s_{2,2,1,1,1} +3325s_{3,1,1,1,1} +525s_{2,1,1,1,1,1} +35s_{1,1,1,1,1,1,1}) +T^8( -56s_{1,1,1,1,1,1,1,1} -980s_{2,1,1,1,1,1,1} -4110s_{2,2,1,1,1,1} -6300s_{2,2,2,1,1} -3131s_{2,2,2,2} -7476s_{3,1,1,1,1,1} -28532s_{3,2,1,1,1} -32254s_{3,2,2,1} -35766s_{3,3,1,1} -27263s_{3,3,2} -32200s_{4,1,1,1,1} -93030s_{4,2,1,1} -58132s_{4,2,2} -92514s_{4,3,1} -26998s_{4,4} -84448s_{5,1,1,1} -161988s_{5,2,1} -83374s_{5,3} -134610s_{6,1,1} -129570s_{6,2} -120498s_{7,1} -46620s_{8})
SSM-Thom polynomial in Schur-tilde functions ( -636S_{3,2,1,1,1} -1569S_{3,2,2,1} -2349S_{3,3,1,1} -1688S_{3,3,2} -965S_{4,1,1,1,1} -8889S_{4,2,1,1} -4432S_{4,2,2} -10857S_{4,3,1} -1715S_{4,4} -9232S_{5,1,1,1} -26404S_{5,2,1} -9464S_{5,3} -23068S_{6,1,1} -20580S_{6,2} -20411S_{7,1} -5796S_{8} -59S_{2,2,2,1,1} -23S_{2,2,2,2})T^8 +(958S_{3,2,1,1} +527S_{3,2,2} +1115S_{3,3,1} +1296S_{4,1,1,1} +4600S_{4,2,1} +1740S_{4,3} +4794S_{5,1,1} +4632S_{5,2} +5405S_{6,1} +1806S_{7} +21S_{2,2,1,1,1} +91S_{2,2,2,1} +55S_{3,1,1,1,1})T^7 +( -59S_{2,2,1,1} -36S_{2,2,2} -137S_{3,1,1,1} -638S_{3,2,1} -201S_{3,3} -860S_{4,1,1} -924S_{4,2} -1319S_{5,1} -540S_{6})T^6 +(53S_{2,2,1} +124S_{3,1,1} +150S_{3,2} +281S_{4,1} +150S_{5} +9S_{2,1,1,1})T^5 +( -13S_{2,1,1} -15S_{2,2} -47S_{3,1} -36S_{4})T^4 +(5S_{2,1} +6S_{3} +S_{1,1,1})T^3

codimension 4

Local algebra C[x]/(x^5)
Thom-Boardman class \Sigma^{1,1,1,1,0}
Codimension 4
SSM-Thom polynomial in Chern classes (6 c_{4}+ 9 c_{1} c_{3}+ 2 c_{2}^2+ 6 c_{1}^2 T^4(c_{1}^4 +6c_{1}^2c_{2} +9c_{1}c_{3} +2c_{2}^2 +6c_{4}) +T^5( -5c_{1}^5 -40c_{1}^3c_{2} -87c_{1}^2c_{3} -28c_{1}c_{2}^2 -112c_{1}c_{4} -28c_{2}c_{3} -60c_{5}) +T^6(15c_{1}^6 +150c_{1}^4c_{2} +446c_{1}^3c_{3} +144c_{1}^2c_{2}^2 +852c_{1}^2c_{4} +289c_{1}c_{2}c_{3} -c_{2}^3 +897c_{1}c_{5} +127c_{2}c_{4} +51c_{3}^2 +390c_{6}) +T^7( -35c_{1}^7 -420c_{1}^5c_{2} -1620c_{1}^4c_{3} -480c_{1}^3c_{2}^2 -4138c_{1}^3c_{4} -1554c_{1}^2c_{2}c_{3} +92c_{1}c_{2}^3 -6587c_{1}^2c_{5} -1211c_{1}c_{2}c_{4} -678c_{1}c_{3}^2 +111c_{2}^2c_{3} -5768c_{1}c_{6} -371c_{2}c_{5} -441c_{3}c_{4} -2100c_{7}) +T^8(70c_{1}^8 +980c_{1}^6c_{2} +4705c_{1}^5c_{3} +1245c_{1}^4c_{2}^2 +15151c_{1}^4c_{4} +5874c_{1}^3c_{2}c_{3} -725c_{1}^2c_{2}^3 +32726c_{1}^3c_{5} +6057c_{1}^2c_{2}c_{4} +4743c_{1}^2c_{3}^2 -1555c_{1}c_{2}^2c_{3} -90c_{2}^4 +43934c_{1}^2c_{6} +2929c_{1}c_{2}c_{5} +6385c_{1}c_{3}c_{4} -1269c_{2}^2c_{4} -53c_{2}c_{3}^2 +32781c_{1}c_{7} -164c_{2}c_{6} +2325c_{3}c_{5} +569c_{4}^2 +10206c_{8})
SSM-Thom polynomial in Schur functions T^4(24s_{4} +10s_{2,2} +26s_{3,1} +9s_{2,1,1} +s_{1,1,1,1}) +T^5( -360s_{5} -316s_{3,2} -510s_{4,1} -133s_{2,2,1} -265s_{3,1,1} -60s_{2,1,1,1} -5s_{1,1,1,1,1}) +T^6(3360s_{6} +1598s_{3,3} +4554s_{4,2} +5800s_{5,1} +518s_{2,2,2} +3195s_{3,2,1} +3960s_{4,1,1} +729s_{2,2,1,1} +1340s_{3,1,1,1} +225s_{2,1,1,1,1} +15s_{1,1,1,1,1,1}) +T^7( -25200s_{7} -24848s_{4,3} -46784s_{5,2} -50820s_{6,1} -11742s_{3,2,2} -16494s_{3,3,1} -43472s_{4,2,1} -42490s_{5,1,1} -3458s_{2,2,2,1} -16635s_{3,2,1,1} -18900s_{4,1,1,1} -2650s_{2,2,1,1,1} -4725s_{3,1,1,1,1} -630s_{2,1,1,1,1,1} -35s_{1,1,1,1,1,1,1}) +T^8(70s_{1,1,1,1,1,1,1,1} +1470s_{2,1,1,1,1,1,1} +7545s_{2,2,1,1,1,1} +13790s_{2,2,2,1,1} +7555s_{2,2,2,2} +13300s_{3,1,1,1,1,1} +61204s_{3,2,1,1,1} +79583s_{3,2,2,1} +89575s_{3,3,1,1} +75322s_{3,3,2} +67200s_{4,1,1,1,1} +228712s_{4,2,1,1} +157710s_{4,2,2} +259895s_{4,3,1} +83758s_{4,4} +204631s_{5,1,1,1} +448604s_{5,2,1} +256462s_{5,3} +375039s_{6,1,1} +397458s_{6,2} +382326s_{7,1} +166824s_{8})
SSM-Thom polynomial in Schur-tilde functions (56S_{2,2,1,1,1,1} +655S_{2,2,2,1,1} +310S_{2,2,2,2} +125S_{3,1,1,1,1,1} +4442S_{3,2,1,1,1} +10798S_{3,2,2,1} +13653S_{3,3,1,1} +12183S_{3,3,2} +5383S_{4,1,1,1,1} +43803S_{4,2,1,1} +28488S_{4,2,2} +61803S_{4,3,1} +13788S_{4,4} +40228S_{5,1,1,1} +127522S_{5,2,1} +60924S_{5,3} +106534S_{6,1,1} +113158S_{6,2} +113086S_{7,1} +40824S_{8})T^8 +( -170S_{2,2,1,1,1} -500S_{2,2,2,1} -348S_{3,1,1,1,1} -3622S_{3,2,1,1} -2512S_{3,2,2} -4522S_{3,3,1} -4260S_{4,1,1,1} -15314S_{4,2,1} -7590S_{4,3} -15082S_{5,1,1} -17194S_{5,2} -19790S_{6,1} -8400S_{7})T^7 +(14S_{2,1,1,1,1} +180S_{2,2,1,1} +129S_{2,2,2} +358S_{3,1,1,1} +1413S_{3,2,1} +596S_{3,3} +1782S_{4,1,1} +2202S_{4,2} +3006S_{5,1} +1560S_{6})T^6 +( -22S_{2,1,1,1} -76S_{2,2,1} -160S_{3,1,1} -208S_{3,2} -358S_{4,1} -240S_{5})T^5 +(9S_{2,1,1} +10S_{2,2} +26S_{3,1} +24S_{4} +S_{1,1,1,1})T^4
Local algebra C[x,y]/(x^2,y^2)
Thom-Boardman class \Sigma^{2,0}
Codimension 4
SSM-Thom polynomial in Chern classes (-c_{1} c_{3}+ c_{2}^2) T^4+ (-2 c_{2} c_{3}-4 T^4( -c_{1}c_{3} +c_{2}^2) +T^5(4c_{1}^2c_{3} -4c_{1}c_{2}^2 +2c_{1}c_{4} -2c_{2}c_{3}) +T^6( -10c_{1}^3c_{3} +10c_{1}^2c_{2}^2 -11c_{1}^2c_{4} +12c_{1}c_{2}c_{3} -c_{2}^3 -5c_{1}c_{5} +7c_{2}c_{4} -2c_{3}^2) +T^7(20c_{1}^4c_{3} -20c_{1}^3c_{2}^2 +35c_{1}^3c_{4} -42c_{1}^2c_{2}c_{3} +7c_{1}c_{2}^3 +31c_{1}^2c_{5} -44c_{1}c_{2}c_{4} +10c_{1}c_{3}^2 +3c_{2}^2c_{3} +10c_{1}c_{6} -13c_{2}c_{5} +3c_{3}c_{4}) +T^8( -35c_{1}^5c_{3} +35c_{1}^4c_{2}^2 -85c_{1}^4c_{4} +110c_{1}^3c_{2}c_{3} -25c_{1}^2c_{2}^3 -112c_{1}^3c_{5} +164c_{1}^2c_{2}c_{4} -28c_{1}^2c_{3}^2 -21c_{1}c_{2}^2c_{3} -3c_{2}^4 -74c_{1}^2c_{6} +109c_{1}c_{2}c_{5} -21c_{1}c_{3}c_{4} -22c_{2}^2c_{4} +8c_{2}c_{3}^2 -21c_{1}c_{7} +36c_{2}c_{6} -31c_{3}c_{5} +16c_{4}^2)
SSM-Thom polynomial in Schur functions s_{2, 2} T^4+ (-4 s_{2, 2, 1}-6 s_{3, 2}) T^5+ T^4s_{2,2} +T^5( -6s_{3,2} -4s_{2,2,1}) +T^6(19s_{3,3} +25s_{4,2} +9s_{2,2,2} +30s_{3,2,1} +10s_{2,2,1,1}) +T^7( -118s_{4,3} -86s_{5,2} -78s_{3,2,2} -110s_{3,3,1} -144s_{4,2,1} -33s_{2,2,2,1} -88s_{3,2,1,1} -20s_{2,2,1,1,1}) +T^8(35s_{2,2,1,1,1,1} +80s_{2,2,2,1,1} +42s_{2,2,2,2} +200s_{3,2,1,1,1} +320s_{3,2,2,1} +360s_{3,3,1,1} +319s_{3,3,2} +475s_{4,2,1,1} +406s_{4,2,2} +753s_{4,3,1} +253s_{4,4} +550s_{5,2,1} +487s_{5,3} +261s_{6,2})
SSM-Thom polynomial in Schur-tilde functions (3S_{3,2,2,1} +12S_{3,3,1,1} +10S_{3,3,2} +24S_{4,2,1,1} +10S_{4,2,2} +64S_{4,3,1} +13S_{4,4} +50S_{5,2,1} +31S_{5,3} +15S_{6,2})T^8 +( -3S_{3,2,1,1} -4S_{3,2,2} -12S_{3,3,1} -24S_{4,2,1} -15S_{4,3} -11S_{5,2})T^7 +(S_{2,2,2} +8S_{3,2,1} +3S_{3,3} +7S_{4,2})T^6 +( -S_{2,2,1} -3S_{3,2})T^5 +T^4S_{2,2}

codimension 5

Local algebra C[x]/(x^6)
Thom-Boardman class \Sigma^{1,1,1,1,1,0}
Codimension 5
SSM-Thom polynomial in Chern classes (c_{1}^5+ 10 c_{1}^3 c_{2}+ 25 c_{1}^2 c_{3}+ T^5(c_{1}^5 +10c_{1}^3c_{2} +25c_{1}^2c_{3} +10c_{1}c_{2}^2 +38c_{1}c_{4} +12c_{2}c_{3} +24c_{5}) +T^6( -6c_{1}^6 -75c_{1}^4c_{2} -247c_{1}^3c_{3} -113c_{1}^2c_{2}^2 -553c_{1}^2c_{4} -260c_{1}c_{2}c_{3} -12c_{2}^3 -690c_{1}c_{5} -156c_{2}c_{4} -48c_{3}^2 -360c_{6}) +T^7(21c_{1}^7 +315c_{1}^5c_{2} +1317c_{1}^4c_{3} +608c_{1}^3c_{2}^2 +3919c_{1}^3c_{4} +2113c_{1}^2c_{2}c_{3} +93c_{1}c_{2}^3 +7322c_{1}^2c_{5} +2407c_{1}c_{2}c_{4} +817c_{1}c_{3}^2 +108c_{2}^2c_{3} +7624c_{1}c_{6} +1224c_{2}c_{5} +672c_{3}c_{4} +3360c_{7}) +T^8( -56c_{1}^8 -980c_{1}^6c_{2} -5032c_{1}^5c_{3} -2248c_{1}^4c_{2}^2 -18788c_{1}^4c_{4} -10748c_{1}^3c_{2}c_{3} -214c_{1}^2c_{2}^3 -47184c_{1}^3c_{5} -17558c_{1}^2c_{2}c_{4} -6880c_{1}^2c_{3}^2 -522c_{1}c_{2}^2c_{3} +100c_{2}^4 -74386c_{1}^2c_{6} -17106c_{1}c_{2}c_{5} -11242c_{1}c_{3}c_{4} +236c_{2}^2c_{4} -332c_{2}c_{3}^2 -66156c_{1}c_{7} -7056c_{2}c_{6} -4632c_{3}c_{5} -1536c_{4}^2 -25200c_{8})
SSM-Thom polynomial in Schur functions T^5(120s_{5} +92s_{3,2} +154s_{4,1} +35s_{2,2,1} +71s_{3,1,1} +14s_{2,1,1,1} +s_{1,1,1,1,1}) +T^6( -2520s_{6} -1048s_{3,3} -3010s_{4,2} -3954s_{5,1} -305s_{2,2,2} -1926s_{3,2,1} -2415s_{4,1,1} -392s_{2,2,1,1} -720s_{3,1,1,1} -105s_{2,1,1,1,1} -6s_{1,1,1,1,1,1}) +T^7(31920s_{7} +27604s_{4,3} +52266s_{5,2} +58604s_{6,1} +11765s_{3,2,2} +16935s_{3,3,1} +44547s_{4,2,1} +44044s_{5,1,1} +3178s_{2,2,2,1} +15358s_{3,2,1,1} +17395s_{4,1,1,1} +2162s_{2,2,1,1,1} +3815s_{3,1,1,1,1} +441s_{2,1,1,1,1,1} +21s_{1,1,1,1,1,1,1}) +T^8( -56s_{1,1,1,1,1,1,1,1} -1372s_{2,1,1,1,1,1,1} -8268s_{2,2,1,1,1,1} -17346s_{2,2,2,1,1} -10294s_{2,2,2,2} -14336s_{3,1,1,1,1,1} -76392s_{3,2,1,1,1} -110706s_{3,2,2,1} -126300s_{3,3,1,1} -114304s_{3,3,2} -82810s_{4,1,1,1,1} -319788s_{4,2,1,1} -237566s_{4,2,2} -402398s_{4,3,1} -140044s_{4,4} -285404s_{5,1,1,1} -691896s_{5,2,1} -427716s_{5,3} -586138s_{6,1,1} -666452s_{6,2} -662844s_{7,1} -317520s_{8})
SSM-Thom polynomial in Schur-tilde functions ( -382S_{2,2,1,1,1,1} -2353S_{2,2,2,1,1} -1281S_{2,2,2,2} -730S_{3,1,1,1,1,1} -13181S_{3,2,1,1,1} -29533S_{3,2,2,1} -35620S_{3,3,1,1} -34582S_{3,3,2} -14557S_{4,1,1,1,1} -103956S_{4,2,1,1} -76719S_{4,2,2} -155687S_{4,3,1} -43320S_{4,4} -91728S_{5,1,1,1} -296529S_{5,2,1} -167088S_{5,3} -247565S_{6,1,1} -289092S_{6,2} -294860S_{7,1} -126000S_{8})T^8 +(20S_{2,1,1,1,1,1} +437S_{2,2,1,1,1} +1013S_{2,2,2,1} +809S_{3,1,1,1,1} +6148S_{3,2,1,1} +4764S_{3,2,2} +7876S_{3,3,1} +6928S_{4,1,1,1} +23803S_{4,2,1} +13830S_{4,3} +23333S_{5,1,1} +28910S_{5,2} +33470S_{6,1} +16800S_{7})T^7 +( -33S_{2,1,1,1,1} -210S_{2,2,1,1} -165S_{2,2,2} -394S_{3,1,1,1} -1332S_{3,2,1} -680S_{3,3} -1669S_{4,1,1} -2180S_{4,2} -2944S_{5,1} -1800S_{6})T^6 +(92S_{3,2} +154S_{4,1} +120S_{5} +14S_{2,1,1,1} +35S_{2,2,1} +71S_{3,1,1} +S_{1,1,1,1,1})T^5
Local algebra C[x,y]/(xy,x^2+y^3)
Thom-Boardman class \Sigma^{2,0}
Codimension 5
SSM-Thom polynomial in Chern classes T^5( -2c_{1}^2c_{3} +2c_{1}c_{2}^2 -2c_{1}c_{4} +2c_{2}c_{3}) +T^6(10c_{1}^3c_{3} -10c_{1}^2c_{2}^2 +17c_{1}^2c_{4} -14c_{1}c_{2}c_{3} -3c_{2}^3 +10c_{1}c_{5} -9c_{2}c_{4} -c_{3}^2) +T^7( -30c_{1}^4c_{3} +30c_{1}^3c_{2}^2 -74c_{1}^3c_{4} +62c_{1}^2c_{2}c_{3} +12c_{1}c_{2}^3 -87c_{1}^2c_{5} +81c_{1}c_{2}c_{4} -3c_{1}c_{3}^2 +9c_{2}^2c_{3} -40c_{1}c_{6} +41c_{2}c_{5} -c_{3}c_{4}) +T^8(70c_{1}^5c_{3} -70c_{1}^4c_{2}^2 +229c_{1}^4c_{4} -204c_{1}^3c_{2}c_{3} -25c_{1}^2c_{2}^3 +402c_{1}^3c_{5} -389c_{1}^2c_{2}c_{4} +31c_{1}^2c_{3}^2 -58c_{1}c_{2}^2c_{3} +14c_{2}^4 +368c_{1}^2c_{6} -381c_{1}c_{2}c_{5} +33c_{1}c_{3}c_{4} -17c_{2}^2c_{4} -3c_{2}c_{3}^2 +140c_{1}c_{7} -160c_{2}c_{6} +37c_{3}c_{5} -17c_{4}^2)
SSM-Thom polynomial in Schur functions T^5(4s_{3,2} +2s_{2,2,1}) +T^6( -28s_{3,3} -40s_{4,2} -13s_{2,2,2} -40s_{3,2,1} -10s_{2,2,1,1}) +T^7(312s_{4,3} +252s_{5,2} +197s_{3,2,2} +256s_{3,3,1} +358s_{4,2,1} +72s_{2,2,2,1} +176s_{3,2,1,1} +30s_{2,2,1,1,1}) +T^8( -70s_{2,2,1,1,1,1} -235s_{2,2,2,1,1} -151s_{2,2,2,2} -534s_{3,2,1,1,1} -1134s_{3,2,2,1} -1156s_{3,3,1,1} -1228s_{3,3,2} -1614s_{4,2,1,1} -1675s_{4,2,2} -2870s_{4,3,1} -1028s_{4,4} -2294s_{5,2,1} -2132s_{5,3} -1284s_{6,2})
SSM-Thom polynomial in Schur-tilde functions ( -3S_{2,2,2,1,1} -2S_{2,2,2,2} -12S_{3,2,1,1,1} -137S_{3,2,2,1} -138S_{3,3,1,1} -182S_{3,3,2} -252S_{4,2,1,1} -303S_{4,2,2} -644S_{4,3,1} -136S_{4,4} -584S_{5,2,1} -460S_{5,3} -292S_{6,2})T^8 +(10S_{2,2,2,1} +32S_{3,2,1,1} +52S_{3,2,2} +72S_{3,3,1} +134S_{4,2,1} +100S_{4,3} +92S_{5,2})T^7 +( -2S_{2,2,1,1} -5S_{2,2,2} -22S_{3,2,1} -12S_{3,3} -24S_{4,2})T^6 +(2S_{2,2,1} +4S_{3,2})T^5

codimension 6

Local algebra C[x]/(x^7)
Thom-Boardman class \Sigma^{1,1,1,1,1,1,0}
Codimension 6
SSM-Thom polynomial in Chern classes T^6(c_{1}^6 +15c_{1}^4c_{2} +55c_{1}^3c_{3} +30c_{1}^2c_{2}^2 +141c_{1}^2c_{4} +79c_{1}c_{2}c_{3} +5c_{2}^3 +202c_{1}c_{5} +55c_{2}c_{4} +17c_{3}^2 +120c_{6}) +T^7( -7c_{1}^7 -126c_{1}^5c_{2} -576c_{1}^4c_{3} -334c_{1}^3c_{2}^2 -1952c_{1}^3c_{4} -1290c_{1}^2c_{2}c_{3} -118c_{1}c_{2}^3 -4175c_{1}^2c_{5} -1765c_{1}c_{2}c_{4} -532c_{1}c_{3}^2 -171c_{2}^2c_{3} -4986c_{1}c_{6} -1089c_{2}c_{5} -519c_{3}c_{4} -2520c_{7}) +T^8(28c_{1}^8 +588c_{1}^6c_{2} +3263c_{1}^5c_{3} +1903c_{1}^4c_{2}^2 +13823c_{1}^4c_{4} +9846c_{1}^3c_{2}c_{3} +901c_{1}^2c_{2}^3 +39534c_{1}^3c_{5} +19747c_{1}^2c_{2}c_{4} +6236c_{1}^2c_{3}^2 +2565c_{1}c_{2}^2c_{3} +71234c_{1}^2c_{6} +23891c_{1}c_{2}c_{5} +11945c_{1}c_{3}c_{4} +1315c_{2}^2c_{4} +857c_{2}c_{3}^2 +72692c_{1}c_{7} +12588c_{2}c_{6} +5767c_{3}c_{5} +1997c_{4}^2 +31920c_{8})
SSM-Thom polynomial in Schur functions T^6(720s_{6} +266s_{3,3} +770s_{4,2} +1044s_{5,1} +70s_{2,2,2} +455s_{3,2,1} +580s_{4,1,1} +84s_{2,2,1,1} +155s_{3,1,1,1} +20s_{2,1,1,1,1} +s_{1,1,1,1,1,1}) +T^7( -20160s_{7} -15524s_{4,3} -29648s_{5,2} -34272s_{6,1} -6044s_{3,2,2} -8902s_{3,3,1} -23458s_{4,2,1} -23548s_{5,1,1} -1514s_{2,2,2,1} -7393s_{3,2,1,1} -8400s_{4,1,1,1} -936s_{2,2,1,1,1} -1645s_{3,1,1,1,1} -168s_{2,1,1,1,1,1} -7s_{1,1,1,1,1,1,1}) +T^8(28s_{1,1,1,1,1,1,1,1} +784s_{2,1,1,1,1,1,1} +5403s_{2,2,1,1,1,1} +12686s_{2,2,2,1,1} +8039s_{2,2,2,2} +9282s_{3,1,1,1,1,1} +55828s_{3,2,1,1,1} +88317s_{3,2,2,1} +102114s_{3,3,1,1} +97939s_{3,3,2} +60200s_{4,1,1,1,1} +257655s_{4,2,1,1} +203121s_{4,2,2} +352227s_{4,3,1} +130582s_{4,4} +230762s_{5,1,1,1} +606318s_{5,2,1} +398938s_{5,3} +521976s_{6,1,1} +627144s_{6,2} +643608s_{7,1} +332640s_{8})
SSM-Thom polynomial in Schur-tilde functions (198496S_{4,3,1} +64890S_{4,4} +113404S_{5,1,1,1} +361242S_{5,2,1} +227324S_{5,3} +306480S_{6,1,1} +378618S_{6,2} +394668S_{7,1} +191520S_{8} +27S_{2,1,1,1,1,1,1} +887S_{2,2,1,1,1,1} +3808S_{2,2,2,1,1} +2303S_{2,2,2,2} +1576S_{3,1,1,1,1,1} +19176S_{3,2,1,1,1} +39631S_{3,2,2,1} +47112S_{3,3,1,1} +47668S_{3,3,2} +20485S_{4,1,1,1,1} +129085S_{4,2,1,1} +102578S_{4,2,2})T^8 +( -46S_{2,1,1,1,1,1} -456S_{2,2,1,1,1} -898S_{2,2,2,1} -810S_{3,1,1,1,1} -4856S_{3,2,1,1} -4014S_{3,2,2} -6284S_{3,3,1} -5460S_{4,1,1,1} -17588S_{4,2,1} -11380S_{4,3} -17516S_{5,1,1} -22666S_{5,2} -26568S_{6,1} -15120S_{7})T^7 +(20S_{2,1,1,1,1} +84S_{2,2,1,1} +70S_{2,2,2} +155S_{3,1,1,1} +455S_{3,2,1} +266S_{3,3} +580S_{4,1,1} +770S_{4,2} +1044S_{5,1} +720S_{6} +S_{1,1,1,1,1,1})T^6
Local algebra C[x,y]/(xy,x^2+y^4)
Thom-Boardman class \Sigma^{2,0}
Codimension 6
SSM-Thom polynomial in Chern classes T^6( -2c_{1}^3c_{3} +2c_{1}^2c_{2}^2 -5c_{1}^2c_{4} +2c_{1}c_{2}c_{3} +3c_{2}^3 -6c_{1}c_{5} +9c_{2}c_{4} -3c_{3}^2) +T^7(12c_{1}^4c_{3} -12c_{1}^3c_{2}^2 +41c_{1}^3c_{4} -14c_{1}^2c_{2}c_{3} -27c_{1}c_{2}^3 +81c_{1}^2c_{5} -86c_{1}c_{2}c_{4} +34c_{1}c_{3}^2 -29c_{2}^2c_{3} +54c_{1}c_{6} -67c_{2}c_{5} +13c_{3}c_{4}) +T^8( -42c_{1}^5c_{3} +42c_{1}^4c_{2}^2 -184c_{1}^4c_{4} +68c_{1}^3c_{2}c_{3} +116c_{1}^2c_{2}^3 -507c_{1}^3c_{5} +466c_{1}^2c_{2}c_{4} -205c_{1}^2c_{3}^2 +249c_{1}c_{2}^2c_{3} -3c_{2}^4 -664c_{1}^2c_{6} +713c_{1}c_{2}c_{5} -213c_{1}c_{3}c_{4} +123c_{2}^2c_{4} +41c_{2}c_{3}^2 -336c_{1}c_{7} +400c_{2}c_{6} -60c_{3}c_{5} -4c_{4}^2)
SSM-Thom polynomial in Schur functions T^6(4s_{3,3} +16s_{4,2} +5s_{2,2,2} +12s_{3,2,1} +2s_{2,2,1,1}) +T^7( -196s_{4,3} -244s_{5,2} -160s_{3,2,2} -140s_{3,3,1} -282s_{4,2,1} -51s_{2,2,2,1} -104s_{3,2,1,1} -12s_{2,2,1,1,1}) +T^8(42s_{2,2,1,1,1,1} +242s_{2,2,2,1,1} +197s_{2,2,2,2} +468s_{3,2,1,1,1} +1408s_{3,2,2,1} +1074s_{3,3,1,1} +1477s_{3,3,2} +1902s_{4,2,1,1} +2422s_{4,2,2} +3232s_{4,3,1} +1060s_{4,4} +3396s_{5,2,1} +2800s_{5,3} +2256s_{6,2})
SSM-Thom polynomial in Schur-tilde functions (27S_{2,2,2,1,1} +29S_{2,2,2,2} +60S_{3,2,1,1,1} +456S_{3,2,2,1} +318S_{3,3,1,1} +529S_{3,3,2} +646S_{4,2,1,1} +992S_{4,2,2} +1356S_{4,3,1} +308S_{4,4} +1598S_{5,2,1} +1188S_{5,3} +1032S_{6,2})T^8 +( -2S_{2,2,1,1,1} -23S_{2,2,2,1} -50S_{3,2,1,1} -97S_{3,2,2} -80S_{3,3,1} -186S_{4,2,1} -116S_{4,3} -164S_{5,2})T^7 +(2S_{2,2,1,1} +5S_{2,2,2} +12S_{3,2,1} +4S_{3,3} +16S_{4,2})T^6
Local algebra C[x,y]/(xy,x^3+y^3)
Thom-Boardman class \Sigma^{2,0}
Codimension 6
SSM-Thom polynomial in Chern classes T^6( -c_{1}^3c_{3} +c_{1}^2c_{2}^2 -2c_{1}^2c_{4} +3c_{1}c_{2}c_{3} -c_{2}^3 -3c_{2}c_{4} +3c_{3}^2) +T^7(6c_{1}^4c_{3} -6c_{1}^3c_{2}^2 +17c_{1}^3c_{4} -21c_{1}^2c_{2}c_{3} +4c_{1}c_{2}^3 +10c_{1}^2c_{5} +17c_{1}c_{2}c_{4} -30c_{1}c_{3}^2 +3c_{2}^2c_{3} +17c_{2}c_{5} -17c_{3}c_{4}) +T^8( -21c_{1}^5c_{3} +21c_{1}^4c_{2}^2 -78c_{1}^4c_{4} +90c_{1}^3c_{2}c_{3} -12c_{1}^2c_{2}^3 -92c_{1}^3c_{5} -37c_{1}^2c_{2}c_{4} +149c_{1}^2c_{3}^2 -23c_{1}c_{2}^2c_{3} +3c_{2}^4 -40c_{1}^2c_{6} -124c_{1}c_{2}c_{5} +174c_{1}c_{3}c_{4} -9c_{2}^2c_{4} -c_{2}c_{3}^2 -70c_{2}c_{6} +54c_{3}c_{5} +16c_{4}^2)
SSM-Thom polynomial in Schur functions T^6(6s_{3,3} +2s_{4,2} +3s_{3,2,1} +s_{2,2,1,1}) +T^7( -96s_{4,3} -26s_{5,2} -24s_{3,2,2} -75s_{3,3,1} -51s_{4,2,1} -8s_{2,2,2,1} -31s_{3,2,1,1} -6s_{2,2,1,1,1}) +T^8(21s_{2,2,1,1,1,1} +51s_{2,2,2,1,1} +33s_{2,2,2,2} +150s_{3,2,1,1,1} +262s_{3,2,2,1} +468s_{3,3,1,1} +435s_{3,3,2} +399s_{4,2,1,1} +363s_{4,2,2} +1179s_{4,3,1} +590s_{4,4} +462s_{5,2,1} +842s_{5,3} +192s_{6,2})
SSM-Thom polynomial in Schur-tilde functions (6S_{2,2,2,1,1} +4S_{2,2,2,2} +21S_{3,2,1,1,1} +74S_{3,2,2,1} +133S_{3,3,1,1} +132S_{3,3,2} +134S_{4,2,1,1} +124S_{4,2,2} +520S_{4,3,1} +210S_{4,4} +187S_{5,2,1} +356S_{5,3} +66S_{6,2})T^8 +( -S_{2,2,1,1,1} -4S_{2,2,2,1} -16S_{3,2,1,1} -12S_{3,2,2} -45S_{3,3,1} -33S_{4,2,1} -64S_{4,3} -16S_{5,2})T^7 +(S_{2,2,1,1} +2S_{4,2} +3S_{3,2,1} +6S_{3,3})T^6

codimension 7

Local algebra C[x]/(x^8)
Thom-Boardman class \Sigma^{1,1,1,1,1,1,1,0}
Codimension 7
SSM-Thom polynomial in Chern classes T^7(c_{1}^7 +21c_{1}^5c_{2} +105c_{1}^4c_{3} +70c_{1}^3c_{2}^2 +399c_{1}^3c_{4} +301c_{1}^2c_{2}c_{3} +35c_{1}c_{2}^3 +960c_{1}^2c_{5} +467c_{1}c_{2}c_{4} +139c_{1}c_{3}^2 +58c_{2}^2c_{3} +1284c_{1}c_{6} +326c_{2}c_{5} +154c_{3}c_{4} +720c_{7}) +T^8( -8c_{1}^8 -196c_{1}^6c_{2} -1178c_{1}^5c_{3} -810c_{1}^4c_{2}^2 -5577c_{1}^4c_{4} -4588c_{1}^3c_{2}c_{3} -615c_{1}^2c_{2}^3 -17886c_{1}^3c_{5} -10567c_{1}^2c_{2}c_{4} -3101c_{1}^2c_{3}^2 -1978c_{1}c_{2}^2c_{3} -40c_{2}^4 -36128c_{1}^2c_{6} -14706c_{1}c_{2}c_{5} -6758c_{1}c_{3}c_{4} -1280c_{2}^2c_{4} -712c_{2}c_{3}^2 -41232c_{1}c_{7} -8904c_{2}c_{6} -3720c_{3}c_{5} -1296c_{4}^2 -20160c_{8})

SSM-Thom polynomial in Schur functions T^7(5040s_{7} +3500s_{4,3} +6746s_{5,2} +8028s_{6,1} +1255s_{3,2,2} +1891s_{3,3,1} +4999s_{4,2,1} +5104s_{5,1,1} +294s_{2,2,2,1} +1456s_{3,2,1,1} +1665s_{4,1,1,1} +168s_{2,2,1,1,1} +295s_{3,1,1,1,1} +27s_{2,1,1,1,1,1} +s_{1,1,1,1,1,1,1}) +T^8( -8s_{1,1,1,1,1,1,1,1} -252s_{2,1,1,1,1,1,1} -1950s_{2,2,1,1,1,1} -5033s_{2,2,2,1,1} -3367s_{2,2,2,2} -3332s_{3,1,1,1,1,1} -22226s_{3,2,1,1,1} -37824s_{3,2,2,1} -44330s_{3,3,1,1} -44595s_{3,3,2} -23940s_{4,1,1,1,1} -111758s_{4,2,1,1} -92531s_{4,2,2} -163888s_{4,3,1} -64140s_{4,4} -100772s_{5,1,1,1} -283126s_{5,2,1} -196272s_{5,3} -247968s_{6,1,1} -311700s_{6,2} -329328s_{7,1} -181440s_{8})
SSM-Thom polynomial in Schur-tilde functions ( -125828S_{4,3,1} -46640S_{4,4} -72031S_{5,1,1,1} -222581S_{5,2,1} -151788S_{5,3} -193260S_{6,1,1} -247140S_{6,2} -263052S_{7,1} -141120S_{8} -61S_{2,1,1,1,1,1,1} -861S_{2,2,1,1,1,1} -2891S_{2,2,2,1,1} -1897S_{2,2,2,2} -1481S_{3,1,1,1,1,1} -13557S_{3,2,1,1,1} -26098S_{3,2,2,1} -30942S_{3,3,1,1} -32011S_{3,3,2} -14435S_{4,1,1,1,1} -80943S_{4,2,1,1} -67515S_{4,2,2})T^8 +(27S_{2,1,1,1,1,1} +168S_{2,2,1,1,1} +294S_{2,2,2,1} +295S_{3,1,1,1,1} +1456S_{3,2,1,1} +1255S_{3,2,2} +1891S_{3,3,1} +1665S_{4,1,1,1} +4999S_{4,2,1} +3500S_{4,3} +5104S_{5,1,1} +6746S_{5,2} +8028S_{6,1} +5040S_{7} +S_{1,1,1,1,1,1,1})T^7
Local algebra C[x,y]/(xy,x^2+y^5)
Thom-Boardman class \Sigma^{2,0}
Codimension 7
SSM-Thom polynomial in Chern classes T^7( -2c_{1}^4c_{3} +2c_{1}^3c_{2}^2 -9c_{1}^3c_{4} +9c_{1}c_{2}^3 -26c_{1}^2c_{5} +29c_{1}c_{2}c_{4} -17c_{1}c_{3}^2 +14c_{2}^2c_{3} -24c_{1}c_{6} +34c_{2}c_{5} -10c_{3}c_{4}) +T^8(14c_{1}^5c_{3} -14c_{1}^4c_{2}^2 +79c_{1}^4c_{4} -79c_{1}^2c_{2}^3 +308c_{1}^3c_{5} -279c_{1}^2c_{2}c_{4} +193c_{1}^2c_{3}^2 -208c_{1}c_{2}^2c_{3} -14c_{2}^4 +532c_{1}^2c_{6} -586c_{1}c_{2}c_{5} +258c_{1}c_{3}c_{4} -172c_{2}^2c_{4} -32c_{2}c_{3}^2 +336c_{1}c_{7} -420c_{2}c_{6} +54c_{3}c_{5} +30c_{4}^2)
SSM-Thom polynomial in Schur functions T^7(44s_{4,3} +84s_{5,2} +47s_{3,2,2} +30s_{3,3,1} +82s_{4,2,1} +13s_{2,2,2,1} +24s_{3,2,1,1} +2s_{2,2,1,1,1}) +T^8( -14s_{2,2,1,1,1,1} -121s_{2,2,2,1,1} -121s_{2,2,2,2} -214s_{3,2,1,1,1} -836s_{3,2,2,1} -522s_{3,3,1,1} -855s_{3,3,2} -1102s_{4,2,1,1} -1635s_{4,2,2} -1804s_{4,3,1} -532s_{4,4} -2354s_{5,2,1} -1744s_{5,3} -1788s_{6,2})
SSM-Thom polynomial in Schur-tilde functions ( -1692S_{5,2,1} -1188S_{5,3} -1284S_{6,2} -2S_{2,2,1,1,1,1} -48S_{2,2,2,1,1} -56S_{2,2,2,2} -88S_{3,2,1,1,1} -513S_{3,2,2,1} -306S_{3,3,1,1} -547S_{3,3,2} -678S_{4,2,1,1} -1119S_{4,2,2} -1224S_{4,3,1} -312S_{4,4})T^8 +(2S_{2,2,1,1,1} +13S_{2,2,2,1} +24S_{3,2,1,1} +47S_{3,2,2} +30S_{3,3,1} +82S_{4,2,1} +44S_{4,3} +84S_{5,2})T^7

Local algebra C[x,y]/(xy,x^3+y^4)
Thom-Boardman class \Sigma^{2,0}
Codimension 7
SSM-Thom polynomial in Chern classes T^7( -2c_{1}^4c_{3} +2c_{1}^3c_{2}^2 -7c_{1}^3c_{4} +8c_{1}^2c_{2}c_{3} -c_{1}c_{2}^3 -6c_{1}^2c_{5} -5c_{1}c_{2}c_{4} +13c_{1}c_{3}^2 -2c_{2}^2c_{3} -10c_{2}c_{5} +10c_{3}c_{4}) +T^8(14c_{1}^5c_{3} -14c_{1}^4c_{2}^2 +63c_{1}^4c_{4} -64c_{1}^3c_{2}c_{3} +c_{1}^2c_{2}^3 +97c_{1}^3c_{5} +25c_{1}^2c_{2}c_{4} -128c_{1}^2c_{3}^2 +3c_{1}c_{2}^2c_{3} +3c_{2}^4 +54c_{1}^2c_{6} +126c_{1}c_{2}c_{5} -194c_{1}c_{3}c_{4} +30c_{2}^2c_{4} -16c_{2}c_{3}^2 +94c_{2}c_{6} -63c_{3}c_{5} -31c_{4}^2)
SSM-Thom polynomial in Schur functions (44 s_{4, 3}+ 12 s_{5, 2}+ 9 s_{3, 2, 2}+ 30 T^7(44s_{4,3} +12s_{5,2} +9s_{3,2,2} +30s_{3,3,1} +22s_{4,2,1} +3s_{2,2,2,1} +12s_{3,2,1,1} +2s_{2,2,1,1,1}) +T^8( -14s_{2,2,1,1,1,1} -41s_{2,2,2,1,1} -24s_{2,2,2,2} -118s_{3,2,1,1,1} -222s_{3,2,2,1} -390s_{3,3,1,1} -399s_{3,3,2} -358s_{4,2,1,1} -331s_{4,2,2} -1108s_{4,3,1} -580s_{4,4} -458s_{5,2,1} -880s_{5,3} -204s_{6,2})
SSM-Thom polynomial in Schur-tilde functions ( -2S_{2,2,1,1,1,1} -18S_{2,2,2,1,1} -9S_{2,2,2,2} -52S_{3,2,1,1,1} -129S_{3,2,2,1} -222S_{3,3,1,1} -243S_{3,3,2} -222S_{4,2,1,1} -207S_{4,2,2} -768S_{4,3,1} -360S_{4,4} -312S_{5,2,1} -612S_{5,3} -132S_{6,2})T^8 +(2S_{2,2,1,1,1} +3S_{2,2,2,1} +12S_{3,2,1,1} +9S_{3,2,2} +30S_{3,3,1} +22S_{4,2,1} +44S_{4,3} +12S_{5,2})T^7
Local algebra C[x,y]/(x^2,y^3)
Thom-Boardman class \Sigma^{2,1,0}
Codimension 7
SSM-Thom polynomial in Chern classes T^7( -2c_{1}^2c_{2}c_{3} +2c_{1}c_{2}^3 -4c_{1}c_{2}c_{4} +2c_{1}c_{3}^2 +2c_{2}^2c_{3} -2c_{2}c_{5} +2c_{3}c_{4}) +T^8(10c_{1}^3c_{2}c_{3} -10c_{1}^2c_{2}^3 +27c_{1}^2c_{2}c_{4} -10c_{1}^2c_{3}^2 -14c_{1}c_{2}^2c_{3} -3c_{2}^4 +27c_{1}c_{2}c_{5} -17c_{1}c_{3}c_{4} -6c_{2}^2c_{4} -4c_{2}c_{3}^2 +10c_{2}c_{6} -9c_{3}c_{5} -c_{4}^2)
SSM-Thom polynomial in Schur functions T^7(8s_{4,3} +4s_{5,2} +6s_{3,2,2} +6s_{3,3,1} +6s_{4,2,1} +2s_{2,2,2,1} +2s_{3,2,1,1}) +T^8( -10s_{2,2,2,1,1} -13s_{2,2,2,2} -10s_{3,2,1,1,1} -63s_{3,2,2,1} -50s_{3,3,1,1} -81s_{3,3,2} -50s_{4,2,1,1} -93s_{4,2,2} -148s_{4,3,1} -68s_{4,4} -80s_{5,2,1} -108s_{5,3} -40s_{6,2})
SSM-Thom polynomial in Schur-tilde functions ( -3S_{2,2,2,2} -25S_{3,2,2,1} -18S_{3,3,1,1} -33S_{3,3,2} -18S_{4,2,1,1} -45S_{4,2,2} -76S_{4,3,1} -28S_{4,4} -38S_{5,2,1} -52S_{5,3} -16S_{6,2})T^8 +(6S_{3,2,2} +6S_{3,3,1} +6S_{4,2,1} +8S_{4,3} +4S_{5,2} +2S_{2,2,2,1} +2S_{3,2,1,1})T^7

codimension 8

Local algebra C[x]/(x^9)
Thom-Boardman class \Sigma^{1,1,1,1,1,1,1,1,0}
Codimension 8
SSM-Thom polynomial in Chern classes T^8(c_{1}^8 +28c_{1}^6c_{2} +182c_{1}^5c_{3} +140c_{1}^4c_{2}^2 +952c_{1}^4c_{4} +868c_{1}^3c_{2}c_{3} +140c_{1}^2c_{2}^3 +3383c_{1}^3c_{5} +2229c_{1}^2c_{2}c_{4} +642c_{1}^2c_{3}^2 +501c_{1}c_{2}^2c_{3} +14c_{2}^4 +7552c_{1}^2c_{6} +3455c_{1}c_{2}c_{5} +1559c_{1}c_{3}c_{4} +364c_{2}^2c_{4} +202c_{2}c_{3}^2 +9468c_{1}c_{7} +2314c_{2}c_{6} +954c_{3}c_{5} +332c_{4}^2 +5040c_{8})
SSM-Thom polynomial in Schur functions T^8(s_{1,1,1,1,1,1,1,1} +35s_{2,1,1,1,1,1,1} +300s_{2,2,1,1,1,1} +840s_{2,2,2,1,1} +588s_{2,2,2,2} +511s_{3,1,1,1,1,1} +3732s_{3,2,1,1,1} +6759s_{3,2,2,1} +8031s_{3,3,1,1} +8412s_{3,3,2} +4025s_{4,1,1,1,1} +20259s_{4,2,1,1} +17484s_{4,2,2} +31584s_{4,3,1} +12964s_{4,4} +18424s_{5,1,1,1} +54822s_{5,2,1} +39764s_{5,3} +48860s_{6,1,1} +63808s_{6,2} +69264s_{7,1} +40320s_{8})
SSM-Thom polynomial in Schur-tilde functions (S_{1,1,1,1,1,1,1,1} +35S_{2,1,1,1,1,1,1} +300S_{2,2,1,1,1,1} +840S_{2,2,2,1,1} +588S_{2,2,2,2} +511S_{3,1,1,1,1,1} +3732S_{3,2,1,1,1} +6759S_{3,2,2,1} +8031S_{3,3,1,1} +8412S_{3,3,2} +4025S_{4,1,1,1,1} +20259S_{4,2,1,1} +17484S_{4,2,2} +31584S_{4,3,1} +12964S_{4,4} +18424S_{5,1,1,1} +54822S_{5,2,1} +39764S_{5,3} +48860S_{6,1,1} +63808S_{6,2} +69264S_{7,1} +40320S_{8})T^8
Local algebra C[x,y]/(xy,x^2+y^6)
Thom-Boardman class \Sigma^{2,0}
Codimension 8
SSM-Thom polynomial in Chern classes T^8( -2c_{1}^5c_{3} +2c_{1}^4c_{2}^2 -14c_{1}^4c_{4} -4c_{1}^3c_{2}c_{3} +18c_{1}^2c_{2}^3 -71c_{1}^3c_{5} +60c_{1}^2c_{2}c_{4} -53c_{1}^2c_{3}^2 +57c_{1}c_{2}^2c_{3} +7c_{2}^4 -154c_{1}^2c_{6} +166c_{1}c_{2}c_{5} -90c_{1}c_{3}c_{4} +74c_{2}^2c_{4} +4c_{2}c_{3}^2 -120c_{1}c_{7} +162c_{2}c_{6} -39c_{3}c_{5} -3c_{4}^2)
SSM-Thom polynomial in Schur functions T^8(2s_{2,2,1,1,1,1} +24s_{2,2,2,1,1} +29s_{2,2,2,2} +40s_{3,2,1,1,1} +194s_{3,2,2,1} +108s_{3,3,1,1} +194s_{3,3,2} +250s_{4,2,1,1} +424s_{4,2,2} +406s_{4,3,1} +124s_{4,4} +620s_{5,2,1} +412s_{5,3} +528s_{6,2})
SSM-Thom polynomial in Schur-tilde functions (124S_{4,4} +412S_{5,3} +528S_{6,2} +194S_{3,3,2} +424S_{4,2,2} +406S_{4,3,1} +620S_{5,2,1} +29S_{2,2,2,2} +194S_{3,2,2,1} +108S_{3,3,1,1} +250S_{4,2,1,1} +24S_{2,2,2,1,1} +40S_{3,2,1,1,1} +2S_{2,2,1,1,1,1})T^8
Local algebra C[x,y]/(xy,x^3+y^5)
Thom-Boardman class \Sigma^{2,0}
Codimension 8
SSM-Thom polynomial in Chern classes T^8( -2c_{1}^5c_{3} +2c_{1}^4c_{2}^2 -11c_{1}^4c_{4} +8c_{1}^3c_{2}c_{3} +3c_{1}^2c_{2}^3 -26c_{1}^3c_{5} +7c_{1}^2c_{2}c_{4} +13c_{1}^2c_{3}^2 +10c_{1}c_{2}^2c_{3} -4c_{2}^4 -24c_{1}^2c_{6} -2c_{1}c_{2}c_{5} +34c_{1}c_{3}c_{4} -32c_{2}^2c_{4} +24c_{2}c_{3}^2 -40c_{2}c_{6} +60c_{3}c_{5} -20c_{4}^2)
SSM-Thom polynomial in Schur functions T^8(2s_{2,2,1,1,1,1} +9s_{2,2,2,1,1} +3s_{2,2,2,2} +22s_{3,2,1,1,1} +48s_{3,2,2,1} +66s_{3,3,1,1} +99s_{3,3,2} +82s_{4,2,1,1} +75s_{4,2,2} +232s_{4,3,1} +76s_{4,4} +122s_{5,2,1} +232s_{5,3} +60s_{6,2})
SSM-Thom polynomial in Schur-tilde functions (76S_{4,4} +232S_{5,3} +60S_{6,2} +99S_{3,3,2} +75S_{4,2,2} +232S_{4,3,1} +122S_{5,2,1} +3S_{2,2,2,2} +48S_{3,2,2,1} +66S_{3,3,1,1} +82S_{4,2,1,1} +9S_{2,2,2,1,1} +22S_{3,2,1,1,1} +2S_{2,2,1,1,1,1})T^8
Local algebra C[x,y]/(xy,x^4+y^4)
Thom-Boardman class \Sigma^{2,0}
Codimension 8
SSM-Thom polynomial in Chern classes T^8( -c_{1}^5c_{3} +c_{1}^4c_{2}^2 -5c_{1}^4c_{4} +6c_{1}^3c_{2}c_{3} -c_{1}^2c_{2}^3 -6c_{1}^3c_{5} -9c_{1}^2c_{2}c_{4} +18c_{1}^2c_{3}^2 -5c_{1}c_{2}^2c_{3} +2c_{2}^4 -29c_{1}c_{2}c_{5} +27c_{1}c_{3}c_{4} +13c_{2}^2c_{4} -11c_{2}c_{3}^2 -2c_{2}c_{6} -21c_{3}c_{5} +23c_{4}^2)
SSM-Thom polynomial in Schur functions T^8(s_{2,2,1,1,1,1} +2s_{2,2,2,1,1} +3s_{2,2,2,2} +8s_{3,2,1,1,1} +15s_{3,2,2,1} +36s_{3,3,1,1} +21s_{3,3,2} +23s_{4,2,1,1} +25s_{4,2,2} +95s_{4,3,1} +86s_{4,4} +28s_{5,2,1} +62s_{5,3} +12s_{6,2})
SSM-Thom polynomial in Schur-tilde functions (86S_{4,4} +62S_{5,3} +12S_{6,2} +21S_{3,3,2} +25S_{4,2,2} +95S_{4,3,1} +28S_{5,2,1} +3S_{2,2,2,2} +15S_{3,2,2,1} +36S_{3,3,1,1} +23S_{4,2,1,1} +2S_{2,2,2,1,1} +8S_{3,2,1,1,1} +S_{2,2,1,1,1,1})T^8

Local algebra C[x,y]/(x^2+y^3,xy^2)
Thom-Boardman class \Sigma^{2,1}
Codimension 8
SSM-Thom polynomial in Chern classes T^8( -2c_{1}^3c_{2}c_{3} +2c_{1}^2c_{2}^3 -7c_{1}^2c_{2}c_{4} +2c_{1}^2c_{3}^2 +4c_{1}c_{2}^2c_{3} +c_{2}^4 -9c_{1}c_{2}c_{5} +5c_{1}c_{3}c_{4} +2c_{2}^2c_{4} +2c_{2}c_{3}^2 -4c_{2}c_{6} +3c_{3}c_{5} +c_{4}^2)
SSM-Thom polynomial in Schur functions T^8(2s_{2,2,2,1,1} +3s_{2,2,2,2} +2s_{3,2,1,1,1} +15s_{3,2,2,1} +12s_{3,3,1,1} +21s_{3,3,2} +12s_{4,2,1,1} +25s_{4,2,2} +40s_{4,3,1} +20s_{4,4} +22s_{5,2,1} +32s_{5,3} +12s_{6,2})
SSM-Thom polynomial in Schur-tilde functions (20S_{4,4} +32S_{5,3} +12S_{6,2} +21S_{3,3,2} +25S_{4,2,2} +40S_{4,3,1} +22S_{5,2,1} +3S_{2,2,2,2} +15S_{3,2,2,1} +12S_{3,3,1,1} +12S_{4,2,1,1} +2S_{2,2,2,1,1} +2S_{3,2,1,1,1})T^8